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Engineering Science and Technology, an International Journal xxx (2016) xxx–xxx

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Engineering Science and Technology,an International Journal

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Study on the behaviour of rubber aggregates concrete beams usinganalytical approach

http://dx.doi.org/10.1016/j.jestch.2016.07.0072215-0986/� 2016 The Authors. Published by Elsevier B.V. on behalf of Karabuk University.This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).

⇑ Corresponding author.E-mail addresses: [email protected] (P. Asutkar), sb_shinde@gmail.

com (S.B. Shinde), [email protected] (R. Patel).

Peer review under responsibility of Karabuk University.

Please cite this article in press as: P. Asutkar et al., Study on the behaviour of rubber aggregates concrete beams using analytical approach, Eng. ScInt. J. (2016), http://dx.doi.org/10.1016/j.jestch.2016.07.007

Priyanka Asutkar a,⇑, S.B. Shinde a, Rakesh Patel b

aMGM Jawaharlal Nehru Engineering Collage, Aurangabad, MH, Indiab Sagar Institute of Research Technology and Science, Bhopal, MP, India

a r t i c l e i n f o

Article history:Received 2 April 2016Revised 21 June 2016Accepted 15 July 2016Available online xxxx

Keywords:Rubber aggregatesMethod of initial functionsBeams

a b s t r a c t

Concrete is one the most extensively used construction material all over the world. Many scientists andresearchers are in quest for developing alternate construction material that are environment friendly andcontribute towards sustainable development. Huge amount of rubber tyres waste is being generated dayby day which creates the disposal problem and has many environmental issues. As this scrap rubberwaste is an elastic material having less specific gravity, energy absorbent material can be used as areplacement material for obtaining lightweight concrete. In present study an attempt is made to partiallyreplace the rubber aggregates by coarse aggregates in concrete and to study its impact on properties ofconcrete. A modified concrete is prepared by replacing coarse aggregates in concrete with rubber aggre-gates by varying the replacement proportion from 0% to 20% with increment of 5%. 3 cubes for each per-centage of replacement are casted and tested after 28th days of curing. The physiomechanical propertieslike density, compressive strength and elastic properties of modified concrete are determined from con-crete cubes experimentally and further stresses and displacement at every 50 mm depth of beams aredetermined analytically by method of initial functions (MIF). MIF is an analytical method in which elasticproperties and theoretical loads are used to analyse the beams without conducting any experimental pro-gramme. The analytical results by MIF are compared with bending theory.� 2016 The Authors. Published by Elsevier B.V. on behalf of Karabuk University. This is an open access

article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).

1. Introduction

The scarcity and availability of sand and aggregate at reasonablerates are now giving anxiety to the construction industry. Overyears, deforestation and extraction of natural aggregates from riverbeds, lakes and other water bodies have resulted in huge environ-mental problems. Hence, to prevent pollution authorities areimposing more and more stringent restrictions on the extractionof natural aggregates and its crushing. The best way to overcomethis problem is to find alternate aggregates for construction inplace of conventional natural aggregates. In this research rubberaggregates from discarded tyre rubber in size ranges from 10 to20 mm is partially replaced with natural aggregates in cement con-crete. This attempt of replacing the coarse aggregates with rubber

aggregates will save the natural aggregates, reduces weight ofstructure and also helps achieve sustainability.

1.1. Method of initial functions (MIF)

MIF was first proposed by Malieev in 1951 and further devel-oped by Vlasov in 1955. Beams that are built of more than onematerial are called composite beams. It is difficult to analyse thelaminated beams by the bending theory used for ordinary beams.In MIF, equations governing the flexure of composite laminatedbeams are derived without making any assumption regarding thephysical behaviour of beams. The method of initial functions(MIF) has been used for deriving the equations. It is an analyticalmethod of elasticity theory allows us to obtain the exact solutionsfor certain types of problems without use of hypotheses about thecharacter of the stress strain state of the structural element. Inrecent years the MIF has been used intensively for the analysis ofvarious problems. For example, three dimensional elasticity equa-tions for circular cylindrical shells are solved by assuming Taylorseries expansions for finding stresses and displacements [18].

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Notations

L length of beamH depth of beamb width of beamd density of concreteE Young’s modulus of elasticityF characteristics compressive strength of concrete

G shear modulus of elasticityl Poisson’s ratiov vertical displacementX shear stressrx bending stress

2 P. Asutkar et al. / Engineering Science and Technology, an International Journal xxx (2016) xxx–xxx

2. Literature review

Recycled tyre rubber is used to develop deliberately low elasticmodulus and highly ductile ECC repair material so as to alleviaterepair failure induced by restrained drying shrinkage [1]. Tyreaggregate replaced with coarse aggregate with various percentagesand compared with regular concrete. Fresh and hardened concretestrength were identified [2]. Rubber waste additives reduced bothstatic and dynamic modulus of elasticity [3]. Higher content ofwaste tyre crumb rubber particle used in concrete increases work-ability of concrete and produce the lightweight concrete [4]. Com-pressive strength of concrete with 100% replacement of chippedrubber showed 90% reduction. However reduction in strengthwas 80% when crumb rubber was used as 100% replacement tosand in concrete [5]. The replacement of coarse aggregate by junkrubber in concrete has resulted in reduced compressive strengthand densities [6]. Rubber tyre aggregate were added to M35 mix

Fig. 1. Rubber aggregates 10–20 mm.

Table 1Physical properties of materials used.

Material Specific gravity Bulk density (kg/m3)

Rubber aggregates 1.10 650Fine aggregates 2.6 1650Coarse aggregates 2.8 1720

Table 2Mix proportion (kg/m3).

Replacement % Cement (kg) Water in litres (W/c = 0.50) Fine

0% 364.81 225.17 6105% 437.77 224.2 59010% 437.77 224.2 59015% 437.77 224.2 59020% 437.77 224.2 590

Please cite this article in press as: P. Asutkar et al., Study on the behaviour of ruInt. J. (2016), http://dx.doi.org/10.1016/j.jestch.2016.07.007

with different percentages. Gradual reduction in the compressiveand tensile strength was observed. Upto 8% of rubber aggregatecan be added in the concrete without considerable reduction instrength [7]. Replacement of rubber increased water permeabilitydepth in the concrete and increases the water absorption in caseof coarse aggregate replacement but reduces the water absorptionin case of cement replacement. [8]. Slump value is decreased as thepercentage of replacement of scrap tyre rubber increase sodecrease in workability. Also decrease in compressive, split tensileand flexural strength. In the rubberized concrete the loss ofstrength was 45% with 15% replacement of coarse aggregate withrubber particle [9]. Replacing conventional fine aggregate withcrumb rubber at 10–30%, the unit-weight of concrete can bereduced from 14% up to 28% depending on the type and the contentof the crumb rubber. The concrete exhibits superior thermal and

aggregates (kg) Coarse aggregates (kg) Rubber aggregates (kg)

.43 1239.64 –

.03 1177.65 23.30

.03 1115.67 46.73

.03 1053.69 70.101

.03 991.71 93.46

Fig. 2. Concrete cubes.

Table 3Compressive strength and density of concrete.

% ofreplacement

Ultimateload (kN)

Compressivestrength (N/mm2)

Weight ofcubes in kg

Density inkg/m3

0% 713.25 31.7 8.15 24141.815% 657.67 29.23 7.56 2240.70210% 576.22 25.61 7.23 2143.1415% 480.05 21.34 6.51 1928.8820% 373.72 16.61 6.34 1879.933

bber aggregates concrete beams using analytical approach, Eng. Sci. Tech.,


P. Asutkar et al. / Engineering Science and Technology, an International Journal xxx (2016) xxx–xxx 3

sound properties than plain concrete as measured by the decreasein thermal conductivity coefficient; increase in sound absorptioncoefficient and noise reduction coefficient [10]. Method of initialfunctions is used for two dimensional elasto dynamic problemsfor plain stress and plain strain conditions [11]. MIF has beenapplied for deriving higher order theories for laminated compositethick rectangular plates [12]. Method of initial function is used forthe study of composite beams having two layers of orthotropicmaterial and developed governing equation [13]. Result obtained

(b) Cube with 5% rubber aggregates.

(d) Concrete cube with 15% rubber aggregates.

(a) Cube with no

Fig. 3. Failure of co


with MIF are compared with result obtained by FEM based soft-ware ANSYS and it is observed that they are comparable [14].MIF is successfully applied for the analysis of reinforced concretebrick layer [15]. The method of initial function is used to see theeffect of elastic properties on the behaviour of the beam [16].The deflection obtained by MIF is equal to the deflection obtainedby other theories. The normal stress equal to the intensity of load-ing and shear stress equal to zero at the top of beam are obtain, thisshows that MIF is successfully applied for the analysis of beam

(c) Cube with 10% rubber aggregates.

(e) Concrete cube with 20% rubber aggregates.

rmal concrete.

ncrete cubes.




[17]. MIF gives correct result for both shallow and deep beams.Also in this method it is not necessary to assume the position ofneutral axis; it incorporates the position of neutral axis by itself.Hence it is concluded that analysis done by MIF provides morerealistic behaviour of beam sections of any depth.

3. Material and methods

The material used for experimental work is ordinary Portlandcement (OPC) of grade 53, river sand with a fineness modulus of2.40, natural aggregates and rubber aggregates with a size rangesfrom 10 to 20 mm. The rubbers aggregate shown in Fig. 1 areobtained by shredding the heavy vehicles scrap tyre rubber.

Table 1 shows the physical properties of material required forpreparing the mix proportion of the rubber concrete as shown inTable 2 M25 grade concrete is used. The percentage of replacementis done by volume. For each percentage three specimens of cubessize 150 � 150 � 150 mm are casted and tested after 28 days ofcuring. The casted concrete cubes are shown in Fig. 2.

3.1. Testing of concrete cubes

The concrete cubes were tested according to IS 516:1959 codefor methods of test for strength of concrete. Before testing weight

Table 4Load and elastic properties.

Material % of replacemencoarse aggregat

Coarse aggregates replaced with rubber aggregates concrete 05101520

Table 5Beam loaded with point load 100 kN.

Depth of beam (mm) 0 50 100

MIF V (mm) 0.512 0.512 0.51X (N/mm2) 0.000 0.530 0.81rx (N/mm2) �6.265 �4.580 �2.87

Bending theory V (mm) 0.430 0.430 0.43rx (N/mm2) �7.500 �5.600 �3.75

Table 6Beam loaded with point load 98.80 kN.









of concrete cubes were noted to determine the density of concrete.The concrete cubes are tested on compressive strength testingmachine of 2000 kN capacity. The load is applied without shockand increased continuously at a rate of approximately 140 kg/sq cm/min until the resistance of the specimen to the increasingload breaks down and no greater load can be sustained. The max-imum load applied to the specimen shall then be recorded and theappearance of the concrete and any unusual features in the type offailure are noted (see Table 3).

In Fig. 3 for 0% and 5% replacement ductile failure is observedi.e. extensive plastic deformation and energy absorption beforethe failure. For 10% to 15% replacement elastic failure takes place.When load is applied to the specimen it absorbs more energy butafter failure when the applied load was removed due to rubberaggregates in concrete the cracks formed are recovered to someextent. For 20% replacement propagation of crack is very fast.Cracks propagate nearly perpendicular to the direction of theapplied stress. The ultimate load carried by these specimens is lessbut toughness is more as compared to the other concrete mix.

4. Analysis of composite beam by MIF and bending theory

For finding the stresses and displacement MIF is used. As coarseaggregates are replaced with rubber aggregates in concrete it

t ofes

Load Po (kN) E (N/mm2) G (N/mm2) l

100 28729.13 1197.47 0.2098.80 24658.06 10274.19 0.2097.50 21589.82 8995.75 0.2093.20 16827.65 7011.52 0.2085.20 14284.55 5951.89 0.20

150 200 250 300 350 400

2 0.511 0.511 0.511 0.511 0.510 0.5110 0.930 0.960 0.920 0.790 0.510 0.0000 �1.800 0.481 1.985 3.930 5.740 7.670

0 0.430 0.430 0.430 0.430 0.430 0.4300 �1.900 0.000 1.900 3.750 5.600 7.500

150 200 250 300 350 400

9 0.576 0.576 0.577 0.575 0.575 0.5740 0.880 0.930 0.850 0.670 0.380 0.0001 �1.420 0.370 1.875 3.711 5.575 7.530

0 0.500 0.500 0.500 0.500 0.500 0.5005 �1.852 0.000 1.852 3.705 5.550 7.410

150 200 250 300 350 400

6 0.646 0.644 0.644 0.641 0.641 0.6410 0.840 0.880 0.810 0.640 0.350 0.0000 �1.372 0.350 1.840 3.685 5.485 7.325

5 0.565 0.565 0.565 0.565 0.565 0.5650 �1.820 0.000 1.820 3.650 5.470 7.310




Depth of beam (mm) 0 50 100 150 200 250 300 350 400

MIF V (mm) 0.805 0.805 0.802 0.802 0.800 0.800 0.800 0.800 0.800X (N/mm2) 0.000 0.390 0.660 0.810 0.850 0.780 0.620 0.350 0.000rx (N/mm2) �6.015 �4.080 �2.560 �1.110 0.290 1.755 3.569 5.450 7.068

Bending theory V (mm) 0.694 0.694 0.694 0.694 0.694 0.694 0.694 0.694 0.694rx (N/mm2) �6.990 �5.240 �3.490 �1.740 0.000 1.740 3.490 5.240 6.990


Depth of beam (mm) 0 50 100 150 200 250 300 350 400

MIF V (mm) 0.919 0.919 0.916 0.915 0.911 0.911 0.910 0.910 0.910X (N/mm2) 0.000 0.380 0.640 0.790 0.830 0.760 0.600 0.340 0.000rx (N/mm2) �5.660 �4.060 �2.540 �1.060 0.150 1.610 3.500 5.130 6.440

Bending theory V (mm) 0.747 0.747 0.747 0.747 0.747 0.747 2.652 0.747 0.747rx (N/mm2) �6.390 �4.790 �2.590 �1.590 0.000 1.590 2.590 4.790 6.390

Fig. 4. (a) Displacement Vs depth of beam by MIF. (b) Displacement Vs depth of beam by bending theory.


Please cite this article in press as: P. Asutkar et al., Study on the behaviour of rubber aggregates concrete beams using analytical approach, Eng. Sci. Tech.,Int. J. (2016), http://dx.doi.org/10.1016/j.jestch.2016.07.007



forms a composite material. The concrete beams of such compositematerials cannot be analysed by the common theories. So in thisstudy MIF is used in which elastic properties and theoretical loadsare used to analyse the beams without conducting any flexural testor experimental programme. The elastic properties (E, G, l) ofmodified concrete are determined from concrete cubes results.The theoretical loads Po are calculated depending on characteristicscompressive strength of cube after 28th days of curing and accord-ing to limit state design of beams. The calculated values theoreticalloads Po are given in Table 4. The modulus of elasticity (E) is deter-mined by using empirical relation E = 0.043d1.5 f 0.5 [01]. This rela-tion depends on characteristic compressive strength and density ofconcrete after 28 days of curing which is applicable for concreteswith densities in the range of 1440–2560 kg/m3. l is constant forall cases and G is determined by using the expression G ¼ E

2ð1þlÞ.

The following values of beam dimensions are chosen for theparticular problem.

H = 400 mm, l = 2000 mm, b = 150 mm.The boundary condition of simply supported edges is given byX = Y = v = 0, at x = 0 and x = l.A point load is assumed, on top surface of the beam. The expres-

sion for point load in sine series is given by

pðxÞ ¼ 2Po

l

X1

n¼1

sinpxl

The stresses and displacement are determined at every 50 mmdepth of beam.

4.1. Analytical results and discussion

The following are analytical results of stresses and displace-ment determined by using the MIF and bending theory. The elasticproperties and loads are used to analyse the beams without con-ducting any experimental programme. The beam is analysed foreach percentage of replacement and the comparison of results byMIF is done with bending theory results.

Tables 5–9 show the analytical results of displacement andstress (both bending and shear) which are determined by usingMIF and bending theory. These results are discussed below by

Fig. 5. Shear stress Vs de


plotting the graphs for each percentage of replacement across thedepth of beam.

Fig. 4 shows variation of displacement across the depth ofbeam. The variation of displacement (v) is almost linear acrossthe depth. It increases with increase in percentage replacementof coarse aggregates by rubber aggregates in concrete. Less vari-ation is observed 5% and 10% but displacement is more for 15%and 20% as compared to normal beam. The displacement resultsby MIF shows the exact displacement i.e. displacement at everydepth of beam varies as compared to the bending theoryresults.

Fig. 5 shows variation of shear stress for different percentage ofreplacement across the depth of beam. There is no need to validatethe results of shear stress with bending theory because the physi-cal conditions of beam that shear stress is maximum at centre andzero at support of beam is exactly satisfied. As percentage replace-ment of coarse aggregates by rubber aggregates in concreteincreases the shear stress decreases.

Fig. 6 shows variation of bending stress across the depth ofbeam for different percentage of replacement. The profile of graphsshows that results from MIF and bending theory are nearly samewith less difference. According to bending theory the bendingstress should be zero at neutral axis and maximum at top fibres,but the results by MIF shows that the bending stress is not exactlyzero it has some non-zero value. The bending stress decreases asthe percentage replacement of coarse aggregates by rubber aggre-gates in concrete increases. Reduction of bending stress is less upto 15% but suddenly decreases by 12% for 20% replacement.

4.2. Comparison of MIF and bending theory

Figs. 7 and 8 show results for 5% replacement of coarse aggre-gate with rubber aggregates in concrete. From Fig. 7 it is clear thatfor bending stress the MIF results are nearly equal to bending the-ory results with difference less than 10%. Fig. 8 shows the differ-ence in results of MIF and bending stress which is less than 15%.The graph of displacement results by bending theory is a straightline but the in case of MIF the shape of line is irregular. The analyt-ical results calculated by MIF considering the elastic properties of

pth of beam by MIF.



Fig. 6. (a) Bending stress Vs depth of beam by MIF. (b) Bending stress Vs depth of beam by bending theory.


material due to this the exact variation of stresses and displace-ments across the depth of beam are obtained. While bending the-ory is based on section properties and assumptions.

5. Conclusions

The following conclusions are made based on the above work.It is observed that the specific gravity and bulk density of rub-

ber aggregates are less as compared to natural coarse aggregates.The density of concrete decreases when use of rubber aggregates


in concrete increases. Due to this the lightweight concrete isobtained which helps to reduce the weight of structure. But thecompressive strength decreases and toughness of concreteincreases if use of rubber aggregates increases.

It is found that optimum percentage of replacement of rubberaggregates can be up to 15%. It is concluded that such type of con-crete cannot be used in structural elements where high strength isrequired. It can be used in other construction elements like parti-tion walls, road barriers, pavements, sidewalks, etc. which has highdemand in construction industries.



Fig. 7. Comparison of bending stress.

Fig. 8. Comparison of displacement.


By using MIF it is possible to obtain exact results of stresses anddisplacements. The analytical results calculated by MIF consideringthe elastic properties of material due to this the exact variation ofstresses and displacements across the depth of beam are obtained.While bending theory is based on the assumptions. Hence valida-tion of MIF results with bending theory shows that MIF gives closeto exact results.

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